Suppose after an initial pre-test and a treatment, a group of 30 participants are presented with 10 sentences written in a foreign language, each containing a grammatical error.
To measure participants' performance, we examine what proportion of the 10 errors has been identified on the pre-test, and on the post-test by each participant.
Now, we have a set of 30 proportions for the pre-test, and 30 corresponding proportions for the post-test.
Question
Should one now do a "Paired-Samples t-test" between the proportions on the pre-test and the proportions on the "post-test" OR ALTERNATIVELY one should do a "significance test on the difference between the two (from pre-test, and from post-test) dependent mean proportions"?